Uncertainty estimation by convolution using spatial statistics

Spatial uncertainty modeling of fuzzy information in images for pattern classification

The modeling of the spatial distribution of image properties is important for many pattern recognition problems in science and engineering. Mathematical methods are needed to quantify the variability of this spatial distribution based on which a decision of classification can be made in an optimal sense. However, image properties are often subject to uncertainty due to both incomplete and imprecise information. This paper presents an integrated approach for estimating the spatial uncertainty of vagueness in images using the theory of geostatistics and the calculus of probability measures of fuzzy events. Such a model for the quantification of spatial uncertainty is utilized as a new image feature extraction method, based on which classifiers can be trained to perform the task of pattern recognition. Applications of the proposed algorithm to the classification of various types of image data suggest the usefulness of the proposed uncertainty modeling technique for texture feature extraction.

Analytical determination of the uncertainty and the optimum sampling frequency for one-dimensional images with noise

Kriging is an estimation technique that has been proved useful in image processing since it behaves, under regular sampling, as a convolution. The uncertainty obtained with kriging has also been shown to behave as a convolution for the case of regular sampling. The convolution kernel for the uncertainty exclusively depends on the spatial correlation properties of the image. In this work we obtain, first, analytical expressions for the uncertainty of 1D images with noise using this convolution procedure. Then, we use this uncertainty to propose a new criterion for determining whether a 1D image with noise is correctly sampled.

Application of tomographic techniques to the spatial-response mapping of antenna-coupled detectors in the visible

A tomographiclike method based on the inverse radon transform is used to retrieve the irradiance map of a focused laser beam. The results obtained from multiple knife-edge measurements have been processed through a kriging technique. This technique allows us to map both the beam irradiance and the uncertainty associated with the measurement method. The results are compared with those achieved in the standard fitting of two orthogonal knife-edge profiles to a modeled beam. The application of the tomographiclike technique does not require any beam model and produces a higher signal-to-noise ratio than the conventional method. As a consequence, the quality of the estimation of the spatial response map of an antenna-coupled detector in the visible is improved.